-
If a = √x + 2 + √x − 2 , then the value of (a2 – ax) is √x + 2 − √x − 2
-
- 1
- 2
- – 1
- 0
Correct Option: C
| a = | |
| √x + 2 − √x − 2 |
By componendo and dividendo,
| a − 1 |
| = | |
| √x + 2 + √x − 2 − √x + 2 + √x − 2 |
| ⇒ | |
| a − 1 |
| = | = | ||
| 2 √x − 2 | √x − 2 |
On squaring both sides,
| = | = | ||
| a2 − 2a + 1 | x − 2 |
| ⇒ | = | ||
| a2 + 1 − 2a | x − 2 |
By componendo and dividendo,
| = | ||
| 4a | 4 |
| ⇒ | = x | |
| a |
⇒ a2 + 1 = ax
⇒ a2 – ax = – 1
